https://github.com/projecttorreypines/coordinatessystems.jl

https://github.com/projecttorreypines/coordinatessystems.jl

Last synced: 6 months ago
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• Host: GitHub
• URL: https://github.com/projecttorreypines/coordinatessystems.jl
• Owner: ProjectTorreyPines
• License: other
• Created: 2024-03-13T16:49:35.000Z (over 2 years ago)
• Default Branch: master
• Last Pushed: 2024-12-11T01:34:09.000Z (over 1 year ago)
• Last Synced: 2025-03-29T22:28:48.653Z (about 1 year ago)
• Language: Julia
• Size: 572 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# CoordinatesSystems

[![CI](https://github.com/ProjectTorreyPines/CoordinatesSystems.jl/actions/workflows/CI.yml/badge.svg?branch=master)](https://github.com/ProjectTorreyPines/CoordinatesSystems.jl/actions/workflows/CI.yml)

This package provides support to do vectorial computations. 

The first usage is the derivation of metric tensor and associated operators. 

```julia

using CoordinatesSystems, Symbolics

𝐞̂ = UnitBasisVectors(CartesianCS)

@variables r Ψ θ

𝐑 = r * cos(Ψ) * sin(θ) * 𝐞̂.x + r * sin(Ψ) * sin(θ) * 𝐞̂.y + r * cos(θ) * 𝐞̂.z

𝐮 = BasisVectors{SphericalCS}(𝐑, [r, θ, Ψ])

g̅̅ = MetricTensor(𝐮)

r_ = 3.0

θ_ = π / 3

g = g̅̅(r_, θ_, 8.0)

g.r.r == 1.0 && g.θ.θ == r_^2 && g.Ψ.Ψ == r_^2 * sin(θ_)^2

```

```julia

using CoordinatesSystems, Symbolics

@variables r φ z

𝐞 = BasisVectors{CylindricalCS}(r * cos(φ), r * sin(φ),z, [r, φ, z])

𝐯 = PVector{CylindricalCS}(r^3, 0,0)

g̅̅ = MetricTensor(𝐞)

∇ = Divergence(g̅̅)

d = ∇ ⋅ 𝐯

r_ = abs(rand()) +0.0001

isapprox(d(r_, 2.0, 3.0),4 * r_^2, atol=1e-14)

```

The second usage is to perform vectorial calculations on mesh structures. 

```julia

using CoordinatesSystems, Symbolics

nx = 100

ny = 90

arr_gen = ArrayGenerator(nx, ny)

a = 1.0

b = 2.0

𝐮 = PVector{CartesianCS}(arr_gen; fill=a)

𝐯 = PVector{CartesianCS}(arr_gen; fill=b)

M = 𝐮 ⋅ 𝐯

all(M .== 3 * a * b)

A = rand(nx, ny)

B = rand(nx, ny)

C = rand(nx, ny)

𝐮 = PVector{CartesianCS}(A, B, C)

all(norm(𝐮) .== sqrt.(A .^ 2 .+ B .^ 2 .+ C .^ 2))

```